Question

Assuming a normal distribution, families spends an average of $500 on their monthly cell phone bills with a standard deviation of $75. What is the probability a random families' bill is between $350 and $400

Answer 1

There is a 0.02275 to 0.0968 chance that a random family's bill will be between $350 and $400.

Calculating the probability

Provided that,

Mean of the population = 500

The standard deviation(S.D) of the population = 75

Assume,the variable in normal distribution = X

Z= (x- mean)/ S.D

Provided , x = $350 - $400

Z= 350-500/75 = -2(when x=$350)

Z= 400-500/75 = -1.3 (taken x= $400)

The probability that a household will spend between $350 and $400 monthly

P(350>X<400) = P( -2>Z<-1.3)

                        = 0.02275 to 0.0968 (from probability table)

Therefore, the final answer is 0.02275 to 0.0968.

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